Study the following information carefully and answer the questions given below:
An uncertain number of persons sit in a linear row and face north.
Five persons sit between F and M. D sits third to the right of M. A sits four places away from D. More than four persons sit between A and F. K sits second to the right of A and third from one of the extreme ends of the row. Six persons sit between K and G. E sits fifth to the left of G. E sits fourth from one of the extreme ends of the row. As many persons sits to the left of E as to the right of H.

How many persons are there in the row?

The correct answer is 18.

Let us determine the linear arrangement of the persons by setting up a coordinate system where each position in the row is represented by an integer. Let us assume all individuals face North, which means moving to the right corresponds to increasing coordinates and moving to the left corresponds to decreasing coordinates.

1. Let us place M at position 0:

$M=0$

2. "D sits third to the right of M": This means D is placed 3 positions to the right of M:

$D=0+3=3$

3. "Five persons sit between F and M": F can be placed either to the left of M or to the right of M, leaving a gap of 5 positions (so a difference of 6 units in coordinates):
- Case 1: F is to the left of M at position:

$F=-6$

- Case 2: F is to the right of M at position:

$F=6$

4. "A sits four places away from D": This implies the coordinate of A is either 4 units to the left or 4 units to the right of D:
- Sub-case A:

$A=3-4=-1$

- Sub-case B:

$A=3+4=7$

5. "More than four persons sit between A and F": The number of persons between A and F is given by the formula:

$|A-F|-1$

Let us test Case 1 where F = -6:
- If A = -1, the number of persons between A and F is:

$|-1-(-6\left)\right|-1=4$

Since we require more than 4 persons, this position for A is invalid.
- If A = 7, the number of persons between A and F is:

$|7-(-6\left)\right|-1=12$

Since 12 is greater than 4, this arrangement is valid. Thus, we have:

$F=-6$

and

$A=7$

6. "K sits second to the right of A": This puts K at position:

$K=7+2=9$

7. "K sits third from one of the extreme ends of the row": Since we already have positions extending to the left (F is at -6), K must be third from the right extreme end. This means there are exactly 2 positions to the right of K, making the right end of the row position:

$9+2=11$

8. "Six persons sit between K and G": G must be 7 positions away from K (coordinate 9). Since G cannot be to the right of the right end (11), G must sit to the left of K:

$G=9-7=2$

9. "E sits fifth to the left of G": This puts E at position:

$E=2-5=-3$

10. "E sits fourth from one of the extreme ends of the row": Since E is at position -3 and the right end is at 11, E must be fourth from the left extreme end. This means there are exactly 3 positions to the left of E, making the left end of the row position:

$-3-3=-6$

This matches perfectly with the position of F (F = -6 is at the left extreme end).

11. To find the total number of persons in the row, we calculate the number of positions between the left end (-6) and the right end (11):

$\text{Total Persons}=11-(-6)+1=18$

Thus, there are exactly 18 persons sitting in the row.